The polydispersity effect of distributed oxyethylene chains on the cloud points of nonionic surfactants

The cloud points of aqueous solutions containing polyoxyethylene surfactant molecules with a distribution of chain lengths were studied for several nonionic surfactants. Experimentally, the cloud points increased as the oxyethylene chain lengths increased with a linear or logarithmic relation of the number of oxyethylates, as proposed by Schott. An experimental scale, the p-Po scale, was previously developed to correspond to the cloud points, where p is the average number of oxyethylene units per molecule and Po is the shortest chain length reference. However, no previous prediction methods of cloud point addressed systems containing a range of chain lengths. In this work, we propose a rescaling of the representative chain length as s-Po, where s is the cloud point-weighted mean ethylene oxide chain below p, and approximated as (p-Po)/PDI where PDI is the polydispersity index. Using the rescaled length, the experimental data for C(12)Es (lauryl alcohol ethoxylate, LAE), NPE-10 (nonyl phenol ethoxylate) and TDE-10 (tridecyl alcohol ethoxylate) were successfully predicted with no additional parameters, such as {(p-Po)/(PDI)}/CP=a+b{(p-Po)/(PDI)}, where PDI indicates the Broadness of the chain length distribution.